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					10
CHAP TE R 1 0
DETERMINING SAMPLE SIZE
AND THE SAMPLING METHOD
A SURVEY THAT CHANGED
SURVEY SAMPLING
PRACTICE
The Literary Digest, an influential general
interest magazine started in 1890, correctly
predicted several presidential campaigns by
using surveys. The world was becoming
accustomed to viewing surveys as accurate
predictors of future events. But the predic-
tion the magazine made in the 1936 election
was so bad that it is given credit for not only
Literary Digest’sfamous blunder was due to using a poor
sampling method. causing the collapse of the magazine (it was purchased
by Time in 1938) but for stirring interest in refining
surveying sampling techniques.
Alf Landon, the Republican candidate and Governor of
Kansas was running against Democratic President Franklin
D. Roosevelt. The Literary Digest used three lists as its
sample frame for polling American voters. First, it sent a L E ARNI NG OBJ ECTI VE S
■ To become familiar with sample design terminology
■ To learn how to calculate sample size
■ To understand the difference between ―probability‖ and
―nonprobability‖ sampling methods
■ To become acquainted with the specifics of four
probability and four nonprobability sampling techniques
postcard to each of its two million subscribers. Secondly, it added to this sample with
sample
frames composed of lists of telephone owners and automobile owners.
The Digest’ssurvey predicted Landon would win overwhelmingly. Roosevelt won in a
landslide, taking 46 of 48 states. Only Maine and New Hampshire voted for Landon. What
went wrong? The Literary Digesthad used an unusually large sample, yet the results were
ter-
ribly wrong. The answer: the sampling method was wrong. Remember, 1936 was the
depths
of the Great Depression. Those who could afford a magazine subscription, telephone, or
automobile were much better off than the general public, and these ―better off‖ citizens
were much more likely to vote Republican. So the Digestwas surveying, in very large num-
bers, voters who were mostly Republican. They didn’t use a sampling method that would
guarantee that Democratic voters would be just as likely to be surveyed. What this
illustrates
is that you must have a good sampling method. With a poor sampling method, even very
large sample sizes will not produce good survey results. In contrast, other surveys using
much smaller sample sizes predicted Roosevelt would win. They were ridiculed for using
small samples, but their predictions were correct because they used sound sampling meth-
ods. Among those producing accurate predictions was a young man named George Gallup.
The Gallup Company exists today and is still conducting accurate surveys. In this chapter
you
will learn how the sample method is important in producing representative results, and how
the sample size is important in producing accurate survey results.1 292 Chapter 10:
Determining Sample Size and the Sampling Method
■ Where We Are:
1Establish the need for
marketing research
2Define the problem
3Establish research objectives
4Determine research design
5Identify information types
and sources
6Determine methods of
accessing data
7Design data collection forms
8Determine sample plan and
size
9Collect data
10Analyze data
11Prepare and present the final
research report
nternational markets are measured in hundreds of millions of people,
national markets comprise millions of individuals, and even local markets may
constitute hundreds of thousands of households. To obtain information from every
single person in a market is usually impossible and obviously impractical. For these
reasons, marketing researchers make use of a sample. This chapter describes how
researchers go about deciding sample size and taking samples. We begin with defi-
nitions of basic concepts such as population, sample, and census. To be sure, sam-
ple size determination can be complicated,2but we describe a simple way to calcu-
late the desired size of a sample and illustrate how the XL Data Analyst can be used
to do these calculations for you. From here, we describe sample methods and dis-
tinguish four types of probability sampling methods from four types of nonproba-
bility sampling methods. Last, we present a step-by-step procedure for designing
and taking a sample.
BASIC CONCEPTS IN SAMPLES
AND SAMPLING
To begin, we acquaint you with some basic terminology used in sampling. The
populationis the entire group under study as specified by the research project. For
example, a researcher may specify a population as ―heads of households in those
metropolitan areas served by Terminix who are responsible for insect pest control.‖
Asampleis a subset of the population that should represent that entire group. How
large a sample and how to select the sample are the major topics of this chapter. A
censusis defined as an accounting of everyone in the population. Of course, a sam-
ple is used because a census is normally completely unobtainable due to time,
accessibility issues, and cost.
So, researchers must use samples that represent populations, which brings us to
the accuracy concerns that always occur when a sample is taken. Sampling erroris
any error in a survey that occurs because a sample is used. Sampling error is caused
by two factors: (1)the method of sample selection and (2)the size of the sample. As
for the latter, you will learn in this chapter that larger samples represent less sam-
pling error than smaller samples, and that some sampling methods minimize this
error, whereas others do not control it well at all regardless of the size of the sample.
In order to select a sample, you will need a sample frame, which is some master list
of all the members of the population. For instance, if a researcher had defined a
population to be all shoe repair stores in the state of Montana, he or she would need
a master listing of these stores as a frame from which to sample. Similarly, if the pop-
ulation being researched consisted of all certified public accountants (CPAs) in the
United States, a sample frame for this group would be needed. In the case of shoe
repair stores, a list service such as American Business Lists, of Omaha, Nebraska,
which has compiled its list of shoe repair stores from Yellow Pages listings, might be
used. For CPAs, the researcher could use the list of members of the American
Institute of Certified Public Accountants, located in New York City, which contains
a listing of all accountants who have passed the CPA exam. As we all know, lists are
not perfect representations of populations, because new members are added, old
I
■ The population is the entire
group under study as defined by
research objectives. Determining Size of a Sample 293
While directories and phone
books are readily available,
they may have substantial
sample frame error.
ones drop off, and there may be clerical errors in the list. So, researchers understand
thatsample frame error, be it great or small, exists for sample frames in the forms of
mis-, over-, or underrepresentations of the true population in a sample frame.
Whenever a sample is drawn, the amount of potential sample frame error should be
judged by the researcher.3Sometimes the only available sample frame contains
much potential sample frame error, but it is used due to the lack of any other sam-
ple frame. It is a researcher’s responsibility to seek out a sample frame with the least
amount of error at a reasonable cost. The researcher should also apprise the client of
the degree of sample frame error involved.
DETERMINING SIZE OF A SAMPLE
Let’s just focus on the sample error associated with size of the sample. That is, for
now, let’s assume that we can find a sample frame that has an acceptably low level of
sample frame error, and that we can select a sample that is truly representative of the
population. (We will take up sample selection methods after we discuss sample size.)
The Accuracy of a Sample
A convenient way4to describe the amount of sample error due to the size of the
sample, or the accuracy of a sample, is to treat it as a plus-or-minus percentage
value.5That is, we can say that a sample is accurate to ±x%, such as ±5% or ±10%.
The interpretation of sample accuracy uses the following logic: If you use a sample
size with an accuracy level of ±5%, when you analyze your survey’s findings, they
will be about ±5% of what you would find if you performed a census. Let us give an
example of this interpretation, as it is important that you understand how sample
accuracy operates. We will take a sample that is representative of the population of
people who bought birthday gifts in the past year, and let’s say that we find that
50% of our respondents say ―Yes‖ to the question ―The last time you bought a birth-
day gift, did you pay more than $25?‖ With a sample accuracy of ±5%, we can say
that if we took a census of the population of our birthday gift givers, the percent
■ Whenever a sample is taken,
the survey will reflect sampling
error. 294 Chapter 10: Determining Sample Size and the Sampling Method
16%
A
cc
u
ra
cy
Sample Size
Sample Size and Accuracy
From a sample size of 1,000 or
more, very little gain in accuracy
occurs, even with doubling the
sample to 2,000.
14%
12%
10%
8%
6%
4%
2%
0%
50 200 350 500 650 800 950 2,000
1,850
1,700
1,550
1,400
1,250
1,100
Figure 10.1The
Relationship Between
Sample Size and Sample
Accuracy
■ The accuracy of a sample can
be expressed as a ±x% amount.
that will say ―Yes‖ is between 45% and 55% (or 50% ±5%). Think, for a minute,
about the incredible power of a sample: We can interview a subset of the entire pop-
ulation, and we can extrapolate or generalize the sample’s findings to the popula-
tion with a ±x% approximation of what we would find if we took all the time,
energy, and expense to interview every single member of the population.
The relationship between sample size and sample accuracy is presented graph-
ically in Figure10.1. In this figure, sample error (accuracy) is listed on the vertical
axis and sample size is noted on the horizontal one. The graph shows the accuracy
levels of samples ranging in size from 50 to 2,000. The shape of the graph shows
that as the sample size increases, sample error decreases. However, you should
immediately notice that the graph is not a straight line. In other words, doubling
sample size does not result in halving the sample error. The relationship is a curved
one. It looks a bit like a ski jump lying on its back.
There is another important property of the sample accuracy graph. As you look at
the graph, note that at a sample size of around 500, the accuracy level drops below
±5% (it is actually ±4.4%), and it continues to decrease at a very slow rate with
larger sample sizes. In other words, once a sample is greater than, say, 500, large gains
in accuracy are not realized with large increases in the size of the sample. In fact, if it
is already ±4.4% in accuracy, there is not much more accuracy possible.
With the lower end of the sample size axis, however, large gains in accuracy can
be made with a relatively small sample size increase. For example, with a sample size
of 50, the accuracy level is ±13.9%, whereas with a sample size of 250, it is ±6.2%,
meaning the accuracy of the 250 sample is roughly double that of the 50 sample. But
as was just described, such huge gains in accuracy are not the case at the other end
of the sample size scale because of the nature of the curved relationship.
How to Calculate Sample Size
The proper way to calculate sample size is to use the confidence interval formula for
sample sizethat follows.
■ The confidence interval
formula for sample size is the
proper way to determine
sample size.
Sample size formula 􏰄
n z pq
e
=
2
2
( ) Determining Size of a Sample 295
■ Variability refers to how much
respondents agree in their
answer to a question.
If everyone wanted the same
thing on their pizza, there
would be no variability.
Where n =the calculated sample size
z =standard error associated with the chosen level
of confidence (typically, 1.96)
p =estimated percentage in the population
q =(100%−p)
e =acceptable error (desired accuracy level)
The confidence interval formula for sample size is based on three elements:
variability, confidence level, and desired accuracy. We will describe each in turn.
Variability: ptimesq
This formula is used if we are focusing on some categorically scaled question in the
survey. For instance, when conducting a Domino’s Pizza survey, our major concern
might be the percentage of pizza buyers who intend to buy Domino’s. There are two
possible answers: ―yes‖ or ―no.‖ If our pizza buyers population has very little
variability, that is, if almost everyone, say, 90%, are raving Domino’s Pizza fans and
shout ―Yes, yes, yes!‖ then this belief will be reflected in the sample size formula as
90% times 10%, or 900. However, if there is great variability, meaning that no two
respondents agree and we have a 50%/50% split, ptimesqbecomes 50% times 50%,
or 2,500, which is the largest possible ptimesqnumber possible. (There is a differ-
ent formula for when you are trying to estimate an average. However, the percent-
age formula is simpler and more commonly used, so we will restrict our coverage to
the percentage formula.)
The use of p=50%,q=50% is a research industry standard of sorts. As you can
see, it is the most conservative p-qcombination, generating the largest sample size,
so it is preferred when the researcher is uncertain or guessing about the variability.
In fact, public opinion polling companies typically report the accuracy of their
samples, and if you find such a report in a news article or other publication, and
you reconstruct their calculation of their reported sample error, you will find that
they have used 50/50. Alternatively, some researchers opt for a pilot study to deter-
mine the approximate amount of variability.6
PRACTICAL
APPLICATIONS 296 Chapter 10: Determining Sample Size and the Sampling Method
Level of Confidence: z
We need to decide on a level of confidence, and it is customary among marketing
researchers to use the 95% level of confidence, in which the zis 1.96. If a researcher
prefers to use the 99% level of confidence, the corresponding zis 2.58. We will
describe how this level of confidence operates shortly.
Desired Accuracy:e
Lastly, the formula requires that we specify an acceptable level of sample error,
meaning the ±% accuracy notion that we introduced to you. That is, the term eis
the amount of sample error that will be associated with the survey. It is used to indi-
cate how close your sample percentage finding will be to the true population per-
centage if it were repeated many, many times.
Figure10.2illustrates how the level of confidence figures into sample size
accuracy. There is a theoretical notion that if the survey were repeated a great many
times—several thousands of times—and if you plotted the frequency distribution
of each pfor every one of these repeated samples, the pattern would appear as a bell
curve, as you see in Figure10.2. Note that 95% of the replications would fall
between the population p(50% in our example in Figure10.2) and ±e.
Here is an example of a sample size calculation that you can follow to make
certain that you understand how to use the sample size formula. Let us assume
there is great expected variability (50%) and we want ±3% accuracy at the 95%
level of confidence.
■ Desired accuracy of a sample
is expressed as ein the sample
size calculation formula.
–Sample Error
(Desired Accuracy)
±Sample Error (Desired Accuracy)
+Sample Error
(Desired Accuracy)
95% of the replications will fall between
p = 50%
Figure 10.2How Sample
Error and the 95% Level of
Confidence Theoretically
Operate
Sample size computed
withp=50%,q=50%,
ande=3%􏰄
n= ×
=
=
=
196 50 50
3
3842500
9
9600
9
1067
2
2
.()
.(,)
,
, Determining Size of a Sample 297
Whenever you calculate the sample size, you are computing the number of
respondents you should have participate fully in your survey. But invariably, sur-
veys run into two difficulties that require an upward adjustment of the computed
sample size. If you read Marketing Research Application10.1, you will learn about
the two problems of ―incidence rate‖ and ―nonresponse‖ and how to adjust the sam-
ple size to cope with these two problems. You will also find a list of other practical
issues that often force researchers to make sample size adjustments.
Adjusting Your Sample Size to
Compensate for Incidence Rate,
Nonresponse, and More
Suppose that Scope mouthwash wanted to find
out reactions to a new formula that provides for
some whitening of the teeth and a degree of tartar control as
well. The researcher and Scope managers come to agree on a
sample size of 500, so the researcher purchases the names of
500 individuals from a sample supply company. The survey
moves along, but the data collection company that is perform-
ing the telephone interviews reports to the researcher that only
4 out of 5 people in the sample use mouthwash. In other
words, the incidence rate, defined as the percent of individuals
in the sample who qualify to take the survey, is 80%, meaning
that 20%, or 100 names in the sample, are not usable. So, under
this situation, the largest final sample size possible is 400.
At the same time, the data collection company manager
reports to the researcher that potential respondents who
qualify are refusing to take the survey. This problem is referred
to as nonresponse, or failures by qualified respondents to
take part in the survey. The data collection company esti-
mates a refusal rate of 40%, meaning that the response rate is
60%. A response rate of 60% means that only 60% of the 400
qualified respondents will be in the final sample. The
researcher is now faced with a final sample size of 240, far
smaller than the desired size of 500.
To cope with the realities of incidence rate and nonre-
sponse, researchers must make adjustments on their calcu-
lated sample sizes. A simple adjustment formula is as follows.
Adjusted Calculated (1/ (1/
sample =sample ×Incidence×Response
size size rate%) rate %)
Sample size
adjustment
formula 􏰄
If you apply this formula to our Scope
mouthwash example, the computations are as
follows.
Adjusted Calculated (1/Incidence (1/Response
sample size = sample size × rate) × rate)
= 500 × (1/.8) ×(1/.6)
= 500 × 1.25 ×1.67
= 1044
So, as can be seen here, incidence rates and nonresponse
can combine to have a tremendous impact on the final sam-
ple size of a survey, and astute marketing researchers will
make estimates of the magnitudes of these problems and
adjust the calculated sample size accordingly.
There are other factors that may force sample size adjust-
ments. Susie Sangren, President, Clearview Data Strategy, has
contributed the following list of practical constraints that
researchers are likely to encounter:
■ Time pressure. Often research results are needed ―yesterday,‖
meaning that the sample size may be reduced to save time.
■ Cost constraint. A limited amount of money is available for
the study, and limited funds translate to reduced sample size.
■ Study objective. What is the purpose of the study? A decision
that does not need great precision can make do with a very
small sample size such as a few focus groups or a pilot study.
■ Data analysis procedures. Some advanced data-analysis
procedures require much-larger-than-ordinary sample
sizes in order to be fully utilized.a
a
Personal communication to author from Susie Sangren.
Sample size adjustment example 􏰅
MARKETING RESEARCH APPLICATION 10.1 298 Chapter 10: Determining Sample Size and
the Sampling Method
.
Figure 10.3XL Data
Analyst Setup for Sample
Size Calculation
USING THE XL DATA ANALYST TO CALCULATE
SAMPLE SIZE
It is time for you to be introduced to the XL Data Analyst Excel
macro software that accompanies this textbook. There is a more
formal introduction in the following chapter, the first data analysis
chapter in this textbook. The XL Data Analyst is primarily a set of
data analysis procedures that are easy to use and interpret. But
there is a computational aid included in the XL Data Analyst that pertains to sam-
ple size. For now, all you need to do is open up any Excel file that accompanies
this textbook. Because the XL Data Analyst isan Excel macro, you will need to set
the Excel 2003 version security at Medium or Low (Tools—Macros—Security—
checkMediumorLow). Then click on ―Enable Macros‖ when the XL Data Analyst
file loads into Excel. With Excel 2007, enable the macro content via the Security
Warning feature after the file is loaded.
After the file is loaded, you will see a ―Data‖ worksheet and a ―Define Variables‖
worksheet, but you can ignore whatever you see on these worksheets. Instead, use the
XL Data Analyst to access the ―Calculate‖ function available in its main menu. The XL
DataAnalyst will calculate sample size using the confidence sample size formula we
have described in this chapter. As you can see in Figure10.3, we have ―pinned‖ the XL
Data Analyst menu item on the Excel 2007 Quick Access tool bar, and the menu
sequence is Calculate—Sample Size, which opens up the selection window where you
can specify the allowable error (desired sample accuracy) and the estimated percent, p,
value. In our example, we have set the accuracy level at 4% and the estimated pat 60%.
Figure10.4reveals that the XL Data Analyst has computed the sample size
for the 95% level of confidence to be 576, while for the 99% confidence level, the
■ The XL Data Analyst performs
sample size calculations and
provides sensitivity analysis for
variability and sample error.
XLDA Determining Size of a Sample 299
Figure 10.4XL Data
Analyst Sample Size
Calculation Output
calculated sample size is 998. There are two tables following the Sample Size
Table that a researcher can use to inspect the sensitivity of the sample size to
slight variations of e(with estimated pconstant), ranging in our example from
3.0% to 5.0% by .5% increments, or variations in the estimated p(withecon-
stant), ranging from 50% to 70% by 5% increments. The sensitivity analysis
tables are provided so a researcher who is wrestling with a sample size decision
can quickly compare the impact of small differences in his or her assumptions
about variability in the population (p) as well as slightly loosening or tightening
the sample accuracy requirements, or allowable error.
Marketing managers and other clients of marketing researchers do not have a
thorough understanding of sample size. In fact, they tend to have a belief in a false
―law of large sample size.‖ That is, they often confuse the size of the sample with
the representativeness of the sample. As you will soon learn in reading about sam-
ple selection procedures, the way the sample is selected, not its size, determines its
representativeness. Also, as you have just learned, the accuracy benefits of exces-
sively large samples are typically not justified by their increased costs.
It is an ethical marketing researcher’s responsibility to try to educate a client on
the wastefulness of excessively large samples. Occasionally, there are good reasons
for having a very large sample, but whenever the sample size exceeds that of a typ-
ical national opinion poll (1,200 respondents), justification is required. Otherwise,
the manager’s cost will be unnecessarily inflated. Unethical researchers may recom-
mend very large samples as a way to increase their profits, which may be set at a
percentage of the total cost of the survey. They may even have ownership in the
data collection company slated to gather the data at a set cost per respondent. It is
important, therefore, that marketing managers know the motivations underlying
the sample size recommendations of the researchers they hire.

290 - 299).
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HOW TO SELECT A REPRESENTATIVE SAMPLE
You now know that surprisingly few individuals can be chosen in a sample that rep-
resents a population with a small amount of sample error. We now turn to the selec-
tion process, for if the sample selection method is faulty or biased, our findings will
be compromised. For example, if Starbucks Coffee wanted to find out how its cus-
tomers feel about Starbucks coffee and other food products and it used a sample of
customers drawn from those who happened to make a purchase at its Miami
International Airport location on June 12, this sample would not be truly represen-
tative of all Starbucks Coffee customers. It would only represent Starbucks Coffee
customers of that location in that time period.
Probability Sampling Methods
Arandom sampleis one in which every member of the population has an equal
chance, or probability, of being selected into that sample. Sample methods that
embody random sampling are often termed probability sampling methods, because
the chance of selection can be expressed as a probability. We will describe four
probability sampling methods: simple random sampling, systematic sampling, clus-
ter sampling, and stratified sampling. You can use Table10.1as a handy reference,
for it summarizes the basics of each of these sampling techniques. How to Select a
Representative Sample 301
Simple random sampling is like
a lottery because everyone has
an equal chance of being
selected.
■ Simple random sampling
makes use of random numbers to
select each individual into the
sample.
Simple Random Sampling
With simple random sampling, the probability of being selected into the sample is
―known‖ and equal for all members of the population. This sampling technique is
expressed by the following formula:
&#x10fc06;Formula for sample
selection probability
Probability of selection =sample size/population size
So, with simple random sampling, if the researcher was surveying a population
of 100,000 recent DVD player buyers with a sample size of 1,000 respondents, the
probability of selection on any single population member into this sample would be
1,000 divided by 100,000, or 1 out of 100, calculated to be 1%. There are some vari-
ations of simple random sampling, but the table of random numbers technique best
exemplifies simple random sampling.
Therandom numbers techniqueis an application of simple random sampling
that uses the concept of a table of random numbers, which is a listing of numbers
whose nonsystematic (or random) order is assured. Before computer-generated
random numbers were widespread, researchers used physical tables that had num-
bers with no discernible relationship to each other. If you looked at a table of
random numbers, you would not be able to see any systematic sequence of the
numbers regardless of where on the table you began and whether you went up,
down, left, right, or diagonally across the entries.
USING THE XL DATA ANALYST TO GENERATE
RANDOM NUMBERS
You can use the XL Data Analyst to generate your own table of ran-
dom numbers. Figure10.5shows the menu command sequence and
setup window to accomplish this end. Note that the menu sequence
is ―Calculate—Random #’s,‖ and the selection window allows you to
specify how many random integer numbers you want (up to 9,999),
XLDA 302 Chapter 10: Determining Sample Size and the Sampling Method
.
Figure 10.5XL Data
Analyst Setup for Random
Numbers
and you can also specify the largest possible value (up to 999,999,999). In our
example, we have specified 100 random numbers with a maximum value of 1,000.
Figure10.6displays our random numbers. Notice that they are arranged in
five columns. You can experiment with the random-number-table-generator
function of the XL Data Analyst, and you should discover that there is no sys-
tematic pattern relating these numbers to one another.
Figure 10.6XL Data
Analyst Output for
Random Numbers How to Select a Representative Sample 303
■ With a random numbers
technique, you must have unique
number values assigned to all
members of the population.
■ Random digit dialing and the
―plus-one‖ dialing technique
incorporate the simple random
sampling method.
With the random numbers technique, you must have unique number values
assigned to each of the members of your population. You might use social security
numbers because these are unique to each person, or you may have the computer,
such as in a database program, assign unique numbers to them, and do the matching
work to determine what individuals are selected into the sample. Again, the use of
random numbers assures the researcher that every population member who is present
in the master list or file will have an equal chance of being selected into the sample.
If a researcher is using telephone numbers and drawing a sample, this technique
is referred to as random digit dialing. This approach is used in telephone surveys to
overcome the problems of unlisted and new telephone numbers. Unlisted numbers
are a growing concern not only for researchers in the United States but in all
industrialized countries such as those in Europe as well.7In random digit dialing,
telephone numbers are generated randomly with the aid of a computer. Telephone
interviewers call these numbers and administer the survey to the respondent once
the person has been qualified. However, random digit dialing may result in a large
number of calls to nonexisting telephone numbers. A popular variation of random
digit dialing that reduces this problem is the plus-one dialing procedure, in which
numbers are selected from a telephone directory, and a digit, such as a ―1,‖ is added
to each number to determine which telephone number is then dialed.
Systematic Sampling
Before widespread use of computerized databases, researchers used hard-copy lists.
In this situation, systematic samplingis a way to select a simple random sample from a
directory or list that is much more efficient (uses less effort) than with simple ran-
dom sampling, because with a physical list, the researcher must scan all the names to
match up each random number. To apply the systematic sampling technique in the
special case of a physical listing of the population, such as a membership directory or
a telephone book, systematic sampling can be applied with less difficulty and accom-
plished in a shorter time period than can simple random sampling. Furthermore, in
many instances, systematic sampling has the potential to create a sample that is
almost identical in quality to samples created from simple random sampling.
To use systematic sampling, it is necessary to obtain a hard-copy listing of the
population, but it is not necessary to have a unique identification number assigned
to each member on the list. The goal of systematic sampling is to literally ―skip‖
through the list in a systematic way, but to begin at a random starting point in the
list. That is, the research calculates a ―skip interval‖ using the following formula:
&#x10fc06;Formula for skip
interval
Skip interval =population list size/sample size
For example, if the skip interval is calculated to be 100, the researcher will
select every 100th name in the list. This technique is much more efficient than
searching for matches to random numbers. The use of this skip interval formula
ensures that the entire list will be covered. The random sample requirement is
implemented by the use of a random starting point, meaning that the researcher
must use some random number technique to decide on the first name in the sam-
ple. Subsequent names are selected by using the skip interval. Because a random
starting point is used, every name on the list has an equal probability of being
selected into the systematic sample. If you are drawing a systematic sample from a 304
Chapter 10: Determining Sample Size and the Sampling Method
■ Systematic sampling is more
efficient than simple random
sampling, and it ensures random
selection of the sample.
directory of thousands of names, it would be daunting to count to, say, the
44,563rd name, so after pondering a bit, you might realize that you could draw a
single random number from 1 to the number of pages in the directory to randomly
select a page, then draw a random number from 1 to the number of columns on the
page to select the random column, and finally, select a random number between 1
and the number of names in that column. Thus, three quickly drawn random num-
bers would effect the random starting point for your systematic sample.
Cluster Sampling
Another form of probability sampling is known as cluster sampling, in which the
population is divided into subgroups, called ―clusters,‖ each of which represents
the entire population.8Note that the basic concept behind cluster sampling is very
similar to the one described for systematic sampling, but the implementation dif-
fers. The procedure identifies identical clusters. Any one cluster, therefore, will be a
satisfactory representation of the population. Cluster sampling is advantageous
when there is no electronic database of the population. It is easy to administer, and
cluster sampling goes a step further in striving to gain economic efficiency over
simple random sampling by simplifying the sampling procedure used. We illustrate
cluster sampling by describing a type of cluster sample that is sometimes referred to
as ―area sampling.‖
Inarea sampling, the researcher subdivides the population to be surveyed into
geographic areas, such as census tracts, cities, neighborhoods, or any other conve-
nient and identifiable geographic designation. The researcher has two options at
this point: a one-step approach or a two-step approach. In the one-step area sample
approach, the researcher may believe the various geographic areas to be sufficiently
identical to permit him or her to concentrate his or her attention on just one area
and then generalize the results to the full population. But the researcher would
need to select that one area randomly and perform a census of its members.
Alternatively, he or she may employ a two-step area sampleapproach to the sampling
process. That is, for the first step, the researcher could select a random sample of
areas, and then for the second step, he or she could decide on a probability method
to sample individuals within the chosen areas. The two-step area sample approach
is preferable to the one-step approach because there is always the possibility that a
single cluster may be less representative than the researcher believes. But the two-
step method is more costly because more areas and time are involved.9
Stratified Sampling
All of the sampling methods we have described thus far implicitly assume that the
population has a normal or bell-shaped distribution for its key properties. That is,
there is the assumption that every potential sample unit is a fairly good representa-
tion of the population, and any who are extreme in one way are perfectly counter-
balanced by opposite extreme potential sample units. Unfortunately, in marketing
research it is common to work with populations that contain unique subgroupings;
you might encounter a population that is not distributed symmetrically across a
normal curve. With this situation, unless you make adjustments in your sample
design, you will end up with a sample that is inaccurate. One solution is stratified
sampling, which separates the population into different subgroups and then samples
all of these subgroups using a random sampling technique.
■ Area sampling is a practical
application of cluster sampling in
which geographic areas are used
to represent the clusters. How to Select a Representative Sample 305
1
Not at all
To what extent do you value a college degree?
Key:
F Freshmen
S Sophomores
Jr Juniors
Sr Seniors
=
=
=
=
2
F S Jr Sr
Freshmen
mean
345
Very highly
Sophomores
mean
Juniors
mean
Seniors
mean
Figure 10.7Illustration
of Four Strata in a
Stratified Population of
Undergraduate University
Students
For example, let’s take the case of a college that is attempting to assess how its
students perceive the quality of its educational programs. A researcher has formu-
lated the question ―To what extent do you value your college degree?‖ The response
options are along a 5-point scale, where 1 equals ―not valued at all‖ and 5 equals
―very highly valued.‖ The population of students is defined by year: freshman,
sophomore, junior, and senior. It seems reasonable to believe that the averages will
differ by the respondent’s year status because seniors probably value a degree more
than do juniors, who value a degree more than do sophomores, and so on. At the
same time, it is expected that seniors would be more in agreement (have less vari-
ability) than would underclass-persons. This belief is due to the fact that freshmen
are students who are trying out college, some of whom are not serious about com-
pleting it and do not value it highly, but some of whom are intending to become
doctors, lawyers, or professionals whose training will include graduate degree work
as well as their present college work. The serious freshmen students would value a
college degree highly, whereas the less serious ones would not, meaning that we
would find much variability in the freshmen students, less variability in sopho-
mores, still less in juniors, and the least with college seniors.
The situation might be something similar to the distributions illustrated in
Figure10.7. When you look at Figure10.7, you will find that the average score for
each class is successively higher, with freshmen at the lowest average and seniors at
the highest average. Also, the bell-shaped curve for each group, or stratum, is suc-
cessively narrower, meaning that there is great variability in the freshman stratum,
but much less in the senior stratum of our population.
What would happen if we used a simple random sample of equal size for each
of our college groups? Because sample accuracy is determined by the variability in
the population—regardless of whether you assess variability by using ptimesqfor
categorical questions or by using the standard deviation for metric scales—in our
student example, we would be least accurate with freshmen and most accurate with
■ With stratified sampling,
the population is separated into
different strata and a sample is
taken from each stratum. 306 Chapter 10: Determining Sample Size and the Sampling
Method
With stratified sampling, the
researcher identifies subgroups
or strata in the population and
samples each stratum.
seniors. To state this situation differently, we would be statistically overefficient
with seniors and statistically underefficient with freshmen because we would be
oversampling the seniors and undersampling the freshmen. To gain overall statisti-
cal efficiency, we should draw a larger sample of freshmen and a smaller one of
seniors. We might do this by allocating the sample proportionately based on the
total number of the freshmen, sophomores, juniors, and seniors, each taken as a
percentage of the whole college population. (Normally, there are fewer seniors than
juniors than sophomores than freshmen in a college.) Thus, we would be drawing
the smallest sample from the seniors group, who have the least variability in their
assessments of the value of their college education, and the largest sample from the
freshmen, who have the most variability in their assessments. We established in our
sample size calculation section that smaller sample sizes will occur for highly simi-
lar populations (e.g, 90% times 10%), while large sample sizes will be calculated for
highly dissimilar populations (e.g., 50% times 50%).
With stratified sampling, the researcher takes a skewed populationand identifies
the subgroups or stratacontained within it based on their differences. In other
words, each stratum is different from the other strata that make up the entire pop-
ulation. Then simple random sampling, systematic sampling, or some other type of
probability sampling procedure is applied to draw a sample from each stratum. The
stratum sample sizes can differ based on knowledge of the variability in each popu-
lation stratum and with the aim of achieving the greatest overall sample accuracy.
How does stratified sampling result in a more accurate overall sample? There
are two ways this accuracy is achieved. First, stratified sampling allows for explicit
analysis of each stratum. The college degree example illustrates why a researcher
would want to know about the distinguishing differences between the strata in
order to assess the true picture. Each stratum represents a different response pro-
file, and by allocating sample size based on the variability in the strata profiles, a
more efficient sample design is achieved.
Second, there is a procedure that allows the estimation of the overall popula-
tion average by use of a weighted averagefor a stratified sample, whose formula
takes into consideration the sizes of the strata relative to the total population size
and applies those proportions to the strata’s averages. The population average is cal-
culated by multiplying each stratum by its proportion and summing the weighted
■ Stratified sampling separates
the population into dissimilar
groups, called strata, because the
researcher is working with a
skewed population. How to Select a Representative Sample 307
stratum averages. This formula results in an estimate that is consistent with the
true distribution of the population when the sample sizes used in the strata are not
proportionate to their shares of the population. Here is the formula that is used for
two strata:
■ Use a weighted average
formula when combining strata
averages taken in stratified
sampling.
&#x10fc06;Formula for
weighted average
Average
population=(averageA)(proportionA)+(averageB)(proportionB)
where A signifies stratum A, and B signifies stratum B.
Here is an example. A researcher separated a population of households that
rent videos on a regular basis into two strata. Stratum A was families without young
children and stratum B was families with young children. When asked to use a
scale of 1=―poor‖ and 5=―excellent‖ to rate their video rental store on its video
selection, the means were computed to be 2.0 and 4.0, respectively, for the samples.
The researcher knew from census information that families without young children
accounted for 70% of the population, whereas families with young children
accounted for the remaining 30%. The weighted mean rating for video selection
was then computed as (.7)(2.0)+(.3)(4.0)=2.6.
Usually, a surrogate measure, which is some observable or easily determined
characteristic of each population member, is used to help partition or separate the
population members into their various subgroupings. For example, in the
instance of the college, the year classification of each student is a handy surro-
gate. With its internal records, the college could easily identify students in each
stratum, and this determination would be the stratification method. Of course,
there is the opportunity for the researcher to divide the population into as many
relevant strata as necessary to capture different subpopulations. For instance, the
college might want to further stratify on college of study, gender, or grade point
average (GPA) ranges. Perhaps professional-school students value their degrees
more than do liberal arts students, females differently from male students, and
high-GPA students more than average-GPA or failing students. The key issue is
that the researcher should use some basis for dividing the population into strata
that results in different responses across strata. There is no need to stratify if all
strata respond alike.
If the strata sample sizes are faithful to their relative sizes in the population,
you have what is called a proportionate stratified sampledesign. Here you do not use
the weighted formula, because each stratum’s weight is automatically accounted for
by its sample size. But with disproportionate stratified sampling, the weighted for-
mula needs to be used, because the strata sizes do not reflect their relative propor-
tions in the population.
Nonprobability Sampling Methods
The four sampling methods we have described thus far embody probability sam-
pling assumptions. In each case, the probability of any unit being selected from the
population into the sample is known, and it can be calculated precisely given the
sample size, population size, and strata or cluster sizes, if they are used. With a
nonprobability sampling method, selection is not based on fairness, equity, or equal
chance. One author has noted that nonprobability sampling uses human interven-
tion, while probability sampling does not.10In fact, a nonprobability sampling 308 Chapter
10: Determining Sample Size and the Sampling Method
Table10.2
Four Different
Nonprobability
Sampling Techniques
Convenience Sampling
The researcher uses a high-traffic location such as a busy pedestrian area or a shopping
mall
to intercept potential respondents. Sample selection error occurs in the form of the absence
of members of the population who are infrequent or nonusers of that location.
Judgment Sampling
The researcher uses his or her judgment or that of some other knowledgeable person to
identify who will be in the sample. Subjectivity enters in here, and certain members of the
population will have a smaller chance of selection into the sample than will others.
Referral Sampling
Respondents are asked for the names or identities of others like themselves who might
qualify
to take part in the survey. Members of the population who are less well known, disliked, or
whose opinions conflict with the respondent have a low probability of being selected into a
referral sample.
Quota Sampling
The researcher identifies quota characteristics such as demographic or product-use factors
and uses these to set up quotas for each class of respondent. The sizes of the quotas are
determined by the researcher’s belief about the relative size of each class of respondent in
the
population. Often quota sampling is used as a means of ensuring that convenience samples
will have the desired proportions of different respondent classes, thereby reducing the
sample
selection error but not eliminating it.
■ Nonprobability samples do
not embody fairness, equity, or
equal chance.
method is inherently biased, and the researcher acknowledges that the sample is
representative only to some degree that the researcher feels is sufficient under the
circumstances of the survey. To be candid about it, most nonprobability sampling
methods take shortcuts that save effort, time, and money, but which obliterate the
equal-chance guarantee of any probability sampling method. As a result, you can-
not in good conscience calculate the probability of any one person in the popula-
tion being selected into a nonprobability sample.
So, why in the world would a researcher ever want to use a nonprobability sam-
ple? There are three answers to this question, and we just divulged them—effort,
time, and money. Compared to random sampling techniques, nonrandom ones,
meaning nonprobability sampling methods, take less effort, they are faster, and they
cost less. But these savings have a cost that ethical researchers readily acknowledge,
and that cost is diminished representativeness. Nonetheless, it is important that
you become familiar with nonprobability sampling methods as there are instances,
such as when conducting a pretest or a pilot study, when a nonrandom sampling
technique is useful. Alternatively, you should be able to identify when a nonran-
dom sample has been utilized, so that you can make your own informed judgment
as to the representativeness of the sample.
There are four nonprobability sampling methods: convenience samples, judg-
ment samples, referral samples, and quota samples. A discussion of each method
follows, and you can refer to Table10.2, which summarizes how each of these non-
probability sampling techniques operate. How to Select a Representative Sample 309
Convenience Samples
Aconvenience sampleis a sample drawn at the convenience of the researcher or inter-
viewer. Accordingly, the most convenient areas to a researcher in terms of time and
effort turn out to be high-traffic areas such as shopping malls, or busy pedestrian
intersections. The selection of the place and, consequently, prospective respondents
is subjective rather than objective. Certain members of the population are automati-
cally eliminated from the sampling process.11For instance, there are those people
who may be infrequent or even nonvisitors of the particular high-traffic area being
used. On the other hand, in the absence of strict selection procedures, there are mem-
bers of the population who may be omitted because of their physical appearance,
general demeanor, or by the fact that they are in a group rather than alone. One
author states, ―Convenience samples ... can be seriously misleading.‖12
Mall-intercept companies often use a convenience sampling method to recruit
respondents. For example, shoppers are encountered at large shopping malls and
quickly qualified with screening questions. For those satisfying the desired popula-
tion characteristics, a questionnaire may be administered or a taste test performed.
Alternatively, the respondent may be given a test product and asked if he or she
would use it at home. A follow-up telephone call some days later solicits his or her
reaction to the product’s performance. In this case, the convenience extends beyond
easy access of respondents into considerations of setup for taste tests, storage of prod-
ucts to be distributed, and control of the interviewer workforce. Additionally, large
numbers of respondents can be recruited in a matter of days. The screening questions
and geographic dispersion of malls may appear to reduce the subjectivity inherent in
the sample design, but in fact the vast majority of the population was not there and
could not be approached to take part. Yet, there are ways of controlling convenience
sample selection error using a quota system, which we discuss shortly.
Judgment Samples
Ajudgment sampleis somewhat different from a convenience sample in concept
because a judgment sample requires a judgment or an ―educated guess‖ as to who
should represent the population. Often the researcher or some individual helping the
■ A convenience sample relies
on high-traffic areas where some
members of the target
population pass by.
With a convenience sample,
the researcher selects high-
traffic locations and interviews
individuals who happen to be
there. 310 Chapter 10: Determining Sample Size and the Sampling Method
■ Judgment samples rely on
someone specifying what
individuals are typical or judged
to be representative of the
population in some way.
researcher who has considerable knowledge about the population will choose those
individuals that he or she feels constitute the sample. It should be apparent that judg-
ment samples are highly subjective and therefore prone to much error.
However, judgment samples do have special uses. For instance, in the prelimi-
nary stages of a research project, the researcher may use qualitative techniques such
as depth interviews or focus groups as a means of gaining insight and understanding
to the research problem. In this case, judgment sampling is a quick, inexpensive,
and acceptable technique because the researcher is not seeking to generalize the
findings of this sample to the population as a whole. Take, for example, a recent
focus group concerning the need for a low-calorie, low-fat microwave oven cook-
book. Twelve women were selected as representative of the present and prospective
market. Six of these women had owned a microwave oven for 10 or more years, 3 of
the women had owned the oven for less than 10 years, and 3 of the women were in
the market for a microwave oven. In the judgment of the researcher, these 12 women
represented the population adequately for the purposes of the focus group. It must
be quickly pointed out, however, that the intent of this focus group was far different
from the intent of a survey. Consequently, the use of a judgment sample was consid-
ered satisfactory for this particular phase in the research process for the cookbook.
The focus group findings served as the foundation for a large-scale regional survey
conducted two months later that relied on a probability sampling method.
Referral Samples
Areferral sampleis sometimes called a ―snowball sample,‖ because it requires
respondents to provide the names of additional respondents. Such lists begin when
the researcher compiles a short list of potential respondents based on convenience
or judgment. After each respondent is interviewed, he or she is queried about the
names of other possible respondents. In this manner, additional respondents are
referred by previous respondents. Or, as the other name implies, the sample grows
just as a snowball grows when it is rolled downhill.
Referral samples are most appropriate when there is a limited and disappointingly
short sample frame and when respondents can provide the names of others who
would qualify for the survey. For example, some foreign countries have low telephone
penetration or slow mail systems that make these options unsuitable, while a referral
approach adds an element of trust to the approach for each new potential respondent.
The nonprobability aspects of referral sampling come from the selectivity used
throughout. The initial list may also be special in some way, and the primary means of
adding people to the sample is by tapping the memories of those on the original list.
Referral samples are often useful in industrial marketing research situations.13
Quota Samples
We have saved the most commonly used nonprobability sampling method for last.
Thequota sampleestablishes a specific quota for various types of individuals to be
interviewed. The quotas are determined through application of the research objec-
tives and are defined by key characteristics used to identify the population. In the
application of quota sampling, a fieldworker is provided with screening criteria that
will classify the potential respondent into a particular quota cell. For example, if
the interviewer is assigned to obtain a sample quota of 50 each for black females,
black males, white females, and white males, the qualifying characteristics would
be race and gender. Assuming our fieldworkers were conducting mall intercepts,
300 - 310).
<vbk:#page(300)>

■ Referral samples make use of
respondents’ volunteering names
of friends and others whose
names they know
310).
<vbk:#page(310)>

each would determine through visual inspection which category the prospective
respondent fits into, and would work toward filling the quota in each of the four
cells. So a quota system overcomes much of the nonrepresentativeness danger
inherent in convenience samples.14
The popularity of quota samples is attributable to the fact that they combine non-
probability sampling advantages with quota controls that ensure the final sample will
approximate the population with respect to its key characteristics. Quota samples are
often used by consumer goods companies that have a firm grasp on the features char-
acterizing the individuals they wish to study in a particular marketing research proj-
ect. These companies often use mall-intercept data collection companies that deliver
fast service at a reasonable price, and the use of quota controls guarantees that the
final sample will satisfactorily represent the population that the consumer goods
company has targeted for the research project. Quota samples are also used in global
marketing research where communication systems are problematic. For example,
most companies performing research in Latin America use quota samples.15When
done conscientiously and with a firm understanding of the quota characteristics,
quota sampling can rival probability sampling in the minds of some researchers.
ONLINE SAMPLING TECHNIQUES
As you know, Internet surveys are becoming popular. To be sure, sampling for Internet
surveys poses special challenges,16but most of these issues can be addressed in the
context of our probability and nonprobability sampling concepts.17If you understand
how a particular online sampling method works, you can probably interpret the sam-
pling procedure correctly with respect to basic sampling concepts.18For purposes of
illustration, we will describe three types of online sampling: (1)random online inter-
cept sampling, (2)invitation online sampling, and (3)online panel sampling.
Random online intercept samplingrelies on a random selection of Web site visi-
tors. There are a number of Java-based or other html-embedded routines that will
select Web site visitors on a random basis such as time of day or random selection
from the stream of Web site visitors. If the population is defined as Web site visi-
tors, then this is a simple random sample of these visitors within the time frame of
the survey. If the sample selection program starts randomly and incorporates a skip
interval system, it is a systematic sample,19and if the sample program treats the
population of Web site visitors like strata, it uses stratified simple random sampling
as long as random selection procedures are used faithfully. However, if the popula-
tion is other than Web site visitors, and the Web site is used because there are many
visitors, the sample is akin to a mall-intercept sample (convenience sample).
Invitation online samplingis when potential respondents are alerted that they
may fill out a questionnaire that is hosted at a specific Web site.20For example, a
retail store chain may have a notice that is handed to customers with their receipts
notifying them that they may go online to fill out the questionnaire. However, to
avoid spam, online researchers must have an established relationship with potential
respondents who expect to receive an e-mail survey. If the retail store uses a ran-
dom sampling approach such as systematic sampling, a probability sample will
result. Similarly, if the e-mail list is a truly representative group of the population,
and the procedures embody random selection, it will constitute a probability
sample. However, if in either case there is some aspect of the selection procedure
■ Online sampling can be
interpreted in the context of
traditional sampling techniques.
ONLINE 312 Chapter 10: Determining Sample Size and the Sampling Method
that eliminates population members or otherwise overrepresents elements of the
population, the sample will be a nonprobability one.
Online panel samplingrefers to consumer or other respondent panels that are set
up by marketing research companies for the explicit purpose of conducting online
surveys with representative samples. There is a growing number of these compa-
nies, and online panels afford fast, convenient, and flexible access to preprofiled
samples.21Typically, the panel company has several thousand individuals who are
representative of a large geographic area, and the market researcher can specify
sample parameters such as specific geographic representation, income, education,
family characteristics, and so forth. The panel company then uses its database on its
panel members to broadcast an e-mail notification to those panelists who qualify
according to the sample parameters specified by the market researcher. Although
online panel samples are not probability samples, they are used extensively by the
marketing research industry.22In some instances, the online panel company creates
the questionnaire; at other times, the researcher composes the questionnaire on the
panel company’s software, or some other means of questionnaire design might be
used, depending on the services of the panel company. One of the greatest pluses of
online panels is the high response rate, which ensures that the final sample closely
represents the population targeted by the researcher. Other online sampling
approaches are feasible and limited only by the creativity of the sample designers.
SUMMARY
This chapter dealt with the sample aspects of a marketing research survey. We
began by defining basic terms such as sample, population, census, sampling error,
sample frame, and sample frame error. We then described the notions associated
with the confidence interval method of calculating sample size. The formula for
this method requires that the researcher (1)specify a sample accuracy level such as
±3% or ±4%; (2)estimate the variability in the population, which can be taken to
be 50%/50% if the researcher is unsure; and (3)use the 95% or 99% level of confi-
dence. You can calculate sample size with the formula or use the XL Data Analyst.
The chapter then took up sample selection methods, and it described four
probability sampling methods, which are techniques that guarantee that each mem-
ber of the population has an equal chance of being selected into the sample. These
four techniques were: (1)simple random sampling where random numbers are
employed; (2)systematic sampling that utilizes a skip interval for a sample frame
list; (3)cluster sampling if the researcher can identify homogeneous groups in the
population; and (4)stratified sampling, used for skewed populations. Next, four
nonprobability sample methods were described, and it was pointed out for each
one how its application incurs some degree of sample selection error. These tech-
niques were (1)convenience sampling such as using a shopping mall’s customer
traffic as the sample frame; (2)judgment sampling, where someone arbitrarily
specifies who will be in the sample; (3)referral sampling, in which case the respon-
dents divulge the names of friends and acquaintances to the researcher; and
(4)quota sampling, where the researcher attempts to minimize sample selection
error by requiring that certain classes of individuals are in the sample in propor-
tions that are believed to reflect their presence in the population. Review Questions 313
KEY TERMS
Population(p.292)
Sample(p.292)
Census(p.292)
Sampling error(p.292)
Sample frame(p.292)
Sample frame error(p.293)
Accuracy of a sample(p.293)
Confidence interval formula for
sample size(p.294)
Variability(p.295)
Level of confidence(p.296)
Desired accuracy(p.296)
Incidence rate(p.297)
Nonresponse(p.297)
Random sample(p.300)
Probability sampling methods(p.300)
Simple random sampling(p.301)
Random numbers technique(p.301)
Table of random numbers(p.301)
Random digit dialing(p.303)
Plus-one dialing procedure(p.303)
Systematic sampling(p.303)
―Skip interval‖(p.303)
Random starting point(p.303)
Cluster sampling(p.304)
Area sampling(p.304)
One-step area sample(p.304)
Two-step area sample(p.304)
Stratified sampling(p.304)
Skewed population(p.306)
Strata(p.306)
Weighted average(p.306)
Surrogate measure(p.307)
Proportionate stratified sample(p.307)
Disproportionate stratified sampling
(p.307)
Nonprobability sampling method
(p.307)
Convenience sample(p.309)
Judgment sample(p.309)
Referral sample(p.310)
Quota sample(p.310)
Random online intercept sampling
(p.311)
Invitation online sampling(p.311)
Online panel sampling(p.312)
REVI EW QUESTI ONS
1 Define each of the following:
a Population bSample c Census dSample frame
2 Indicate the sample frame error typically found in the households listing of a
telephone book.
3 Explain what is meant by the accuracy of a sample.
4 Why is ptaken to represent the variability of a population?
5 Why is a probability sample also a random sample?
7 How are random numbers vital to a probability sample method?
8 How is sample frame error overcome with a ―plus-one‖ dialing procedure?
9 What single step is critical in preserving the probability characteristic of a sys-
tematic sample? Why?
10 How does cluster sampling differ from stratified sampling?
11 When is a weighted mean required for a stratified sample? Explain when and
why it is not required.
12 What is convenient about a convenience sample?
13 Compare a judgment sample to a referral sample. How are they similar? How
are they unalike? 314 Chapter 10: Determining Sample Size and the Sampling Method
14 In order to implement a quota sample, what prior knowledge does the
researcher need to have about the population?
APPLI CATI ON QUESTI ONS
15 Here are four populations and a potential sample frame for each one. With each pair,
identify: (1)members of the population who are not in the sample frame, and
(2)sample frame items that are not part of the population. Also, for each one, would
you judge the amount of sample frame error to be acceptable or unacceptable?
Population Sample Frame
a. Buyers of Scope mouthwash Mailing list of Consumer Reportssubscribers
b. Listeners of a particular FM radio
classical music station
Telephone directory in your city
Members of Sales and Marketing Executives
International (a national organization of sales
managers)
c. Prospective buyers of a new day planner
and prospective-client tracking kit
d. Users of weatherproof decking
materials (to build outdoor decks)
Individuals’ names registered at a recent home
and garden show
16 Here are some numbers that you can use to sharpen your computational skills for
sample size determination. Crest toothpaste is reviewing plans for its annual sur-
vey of toothpaste purchasers. With each case that follows, calculate the sample
size pertaining to the key variable under consideration. Where information is
missing, provide reasonable assumptions. You can check your computations by
using the sample size calculation feature of the XL Data Analyst.
Acceptable Confidence
Case Key Variable Variability Error Level
1 Market share of Crest 23% share 4% 95%
toothpaste last year
2 Percentage of people who Unknown 5% 99%
brush their teeth per week
3 How likely Crest buyers 30% switched 5% 95%
are to switch brands last year
4 Percentage of people who 20% two years 3.5% 95%
want tartar-control ago; 40% one
features in their toothpaste year ago
5 Willingness of people Unknown 6% 99%
to adopt the toothpaste Application Questions 315
17 Allbookstores.com has a used-textbook division. It buys its books in bulk from
used-book buyers who set up kiosks on college campuses during final exams,
and it sells the used textbooks to students who log on to the Allbookstores.com
Web site via a secured credit card transaction. The used texts are then sent by
United Parcel Service to the student.
The company has conducted a survey of used-book buying by college stu-
dents each year for the past four years. In each survey, 1,000 randomly selected
college students have been asked to indicate whether or not they bought a used
textbook in the previous year. The results are as follows:
Years Ago
1234
Percentage buying used text(s) 70% 60% 55% 50%
What are the sample size implications of these data? That is, assess whether or not
the survey should be continued in the coming year with a sample size of 1,000.
18 Pet Insurers Company markets health and death benefits insurance to pet owners.
It specializes in coverage for pedigreed dogs, cats, and expensive and exotic pets
such as miniature Vietnamese potbellied pigs. The veterinary care costs of these
pets can be high, and their deaths represent substantial financial loss to their own-
ers. A researcher working for Pet Insurers finds that a listing company can provide
a list of 15,000 names that includes all current subscribers to Cat Lovers,Pedigreed
Dog, and Exotic Pets Monthly. If the final sample size is to be 1,000, calculate what
the skip interval should be in a systematic sample for each of the following:
a a telephone survey using drop-down replacement of nonrespondents
b a mail survey with an anticipated 30% response rate (assume the incidence
rate for this sample frame to be 100%)
19 A market researcher is proposing a survey for the Big Tree Country Club, a pri-
vate country club that is contemplating several changes in its layout to make
the golf course more championship caliber. The researcher is considering three
different sample designs as a way to draw a representative sample of the club’s
golfers. The three alternative designs are:
a Station an interviewer at the first-hole tee on one day chosen at random, with
instructions to ask every 10th golfer to fill out a self-administered questionnaire.
b Put a stack of questionnaires on the counter where golfers check in and pay for
their golf carts. There would be a sign above the questionnaires, and there
would be an incentive for a ―free dinner in the clubhouse‖ for three players
who fill out the questionnaires and whose names are selected by a lottery.
c Using the city telephone directory, a plus-one dialing procedure would be
used. With this procedure a random page in the directory would be selected,
and a name on that page would be selected, both using a table of random
numbers. The plus-one system would be applied to that name and every name
listed after it until 1,000 golfers are identified and interviewed by telephone.
Assess the representativeness and other issues associated with this sample
problem. Be sure to identify the sample method being contemplated in each
case. Which sample method do you recommend using and why? 316 Chapter 10:
Determining Sample Size and the Sampling Method
I NTERACTI VE LEARNI NG
You can visit the textbook Web site at www.prenhall.com/burnsbush.
Use the self-study quizzes and get instant feedback on whether or
not you need additional studying to master the material in this chap-
ter. You can also review the chapter’s major points by visiting the
chapter outline and key terms.
CASE 10.1 Peaceful Valley: Trouble in Suburbia
Located on the outskirts of a large city, the suburb of
Peaceful Valley comprises approximately 6,000 upscale
homes. The subdivision came about 10 years ago when
a developer built an earthen dam on Peaceful River and
created Peaceful Lake, a meandering 20-acre body of
water. The lake became the centerpiece of the develop-
ment, and the first 2,000 one-half-acre lots were sold as
lakefront property. Now Peaceful Valley is fully devel-
oped, with 50 streets, all approximately 1.5 miles in
length, with approximately 60 houses on each street.
Peaceful Valley’s residents are primarily young, profes-
sional, dual-income families with one or two school-age
children. A unique feature of Peaceful Valley is that
there are only two entrances/exits, which have security
systems that monitor vehicle traffic. As a result, Peaceful
Valley is considered the safest community in the state.
But controversy has come to Peaceful Valley. The
suburb’s steering committee has recommended that
the community build a swimming pool, tennis court,
and meeting room facility on four adjoining vacant
lots in the back of the subdivision. Construction cost
estimates range from $1.5 million to $2 million,
depending on how large the facility will be. Currently,
every Peaceful Valley homeowner is billed $100 annu-
ally for maintenance, security, and upkeep of Peaceful
Valley. About 75% of the residents pay this fee. To
construct the proposed recreational facility, each
Peaceful Valley household would be expected to pay a
one-time fee of $500, and annual fees would increase
to $200 based on facility maintenance cost estimates.
Objections to the recreational facility come from
various quarters. For some, the one-time fee is unac-
ceptable; for others, the notion of a recreational facil-
ity is not appealing. Some residents have their own
swimming pools, belong to local tennis clubs, or oth-
erwise have little use for a meeting room facility.
Other Peaceful Valley homeowners see the recre-
ational facility as a wonderful addition where they
could have their children learn to swim, play tennis,
or just hang out under supervision.
The president of the Peaceful Valley Suburb
Association has decided to conduct a survey to poll
the opinions and preferences of Peaceful Valley home-
owners regarding the swimming pool, tennis court,
and meeting room facility concept.
1 If the steering committee agrees to a survey that is
accurate to ±5% and at a 95% level of confidence,
what sample size should be used?
2 What sample method do you recommend? In mak-
ing your recommendation, carefully consider the
geographic configuration of Peaceful Valley. Provide
the specifics of how each household in the sample
should be selected, including what provision(s) to
take if a selected household happened to be on
vacation or was unwilling to take part in the survey.
3 Should the survey be a sample (of the size you
calculated in question 1) or a census of Peaceful
Valley homeowners? Defend your choice. Be cer-
tain to discuss any practical considerations that
enter into your choice.
CASE 10.2 Your Integrated Case
College Life E-Zine: Sample Decisions
This is the eighth case in our integrated case series. You
will find the previous College Life E-Zine Cases in
Chapters1, 2, 3, 4, 5, 7,and 9.
Bob Watts is on the phone with Wesley, one of our
hopeful College Life E-Zine owners, discussing the
sample size and selection steps of the survey. Wesley
has volunteered to talk with Bob about this as he is Case 10.2 317
the one who remembers most about this topic from
his undergraduate studies at State U. ―Okay,‖ says
Bob, ―we need to make some decisions that will have
some important consequences about the generaliz-
ability of our survey. As you and the others know, we
have an agreement with State University officials to
have access to their student data files as long as we
provide them with the results of this survey, as they
are very interested in partnering with the College Life
E-Zine. It could off-load a lot of the State U Web site
work that is planned over the next two years. They
said they would work with us in any way possible to
develop a sample of State U students.‖
Wesley says, ―That’s great! I knew they’d be willing
to help us, since my cousin works in the State U Web
site tech area, and he told me a year ago that they had
so much to do that it might take five years to put it all
on State U’s Web site because his area is so under-
funded.‖ Wesley continues, ―I actually consulted my
old marketing research class notes, and I found that
the typical opinion poll has a sample accuracy of from
±3% to ±4%. I will leave it to you to make the recom-
mendation, however. And as for the sample selection,
I’ll trust it to you as well, but since we are using a tele-
phone survey, I found in my notes that random digit
dialing is a commonly used technique. But you’re the
expert, Bob, so whatever you come up with, we’ll give
it strong consideration.‖
Bob Watts says, ―I’ll take all of this under consider-
ation and get back to you and the others next week.
So long for now.‖ Upon switching off his phone, Bob
glances at his calendar and notices that the marketing
research intern he hired from from State U—he has
jotted her first name down—Lori—will meet with
him in three days to begin her five-week rotation in
his group. Somewhat devilishly, Bob thinks, ―I think
I’ll give this Lori a test. I’ll send her an e-mail with the
College Life E-Zine sample decisions that are pend-
ing and see what she comes up with for our initial
interview.‖
Here is Bob’s e-mail to Lori.
To: Lori Baker, Marketing Research Intern
From: Bob Watts, Division Manager
Subject: Initial Interview
Lori:
Some time has passed since we met and I hired you as our
marketing research intern this semester. You are about to
begin your third and last department rotation in the com-
pany and into my department. For your initial interview
with me on Friday, I am providing you with some informa-
tion about a current project, and I would like you to be
prepared to discuss with me your recommendations for cer-
tain sample decisions that must be made very shortly for the
College Life E-Zine project (project proposal attached for
your perusal—I have also included my notes with relevant
communications, including the most recent one concerning
sample size and method with the client group).
1 What is your recommendation as to the sample
size for the survey? I suggest that you use Wesley’s
telephone conversation comments in deciding on
your recommendation.
2 What is your reaction to a random-digit-dialing
approach to select the sample of State U students?
Consider that we will use a data collection com-
pany that can generate random-digit-dialing
numbers easily. Does this alter your reaction to
random digit dialing to any degree?
3 What if one of our budding College Life E-Zine
entrepreneurs is bullish on having us just sample
the technical majors at State U, such as computer
science, computer and electrical engineering,
information systems/decision sciences, computer
graphics, and the like? What is your reaction to
this sample design and why?
4 State U says it will access its electronic student
files to select a sample, but it will only provide us
the sample of students based on our instructions as
to how to select these students. If I assign you the
task of communicating to the State U technical
folks how to select the sample, what steps do you
propose to tell them to take to effect:
aA simple random sample using electronic records?
b A systematic sample using the State University
Student Directory?
Have a good next few days, and I will see you at your
interview at 10:00 a.m. on Friday.
Your task in analyzing this case is to take Lori’s role
and develop answers to each of Bob’s four sampling
questions for the College Life E-Zine survey.
311 - 317).
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